Given the system model in Section , we formulate a sum-rate maximization problem constrained by per-BS transmit power, fronthaul capacity, and practical connectivity constraints. In particular, the connectivity constraints dictate that every user can only be associated with one and only one transmitting cluster. Furthermore, we assume TBSs cannot serve aerial users, which is a practical design consideration since serving aerial users using TBSs requires full-dimensional antenna arrays [1]}, [2]}. The first optimization framework can then be formulated as follows:
\(\max _{\mathbf {w}, \mathbf {z}, \mathbf {r}} \quad & \sum _{ q \in \mathcal {Q}}\sum _{u \in \mathcal {U}} R_{u, q}  \\\textrm {s.t.}&~ (\ref {eq:rate}) \\&\sum _{q \in \mathcal {Q}} z_{u, q} \le 1, ~\forall u \in \mathcal {U} \\& \sum _{q \in \mathcal {Q}_T}\sum _{u \in \mathcal {U}_A} z_{u, q} = 0, \\&\sum _{u \in \mathcal {U}} ||\mathbf {w}_{u,b,q}||_2^2 z_{u, q} \le P_{b,q}, ~ \forall b \in \mathcal {B}_q, \forall q \in \mathcal {Q}\\&\sum _{u \in \mathcal {U}} R_{u, q} \mathbb {1} \lbrace ||\mathbf {w}_{u,b,q}||_2^2\rbrace  \le C_{b, q},\forall b \in \mathcal {B}_q, \forall q \in \mathcal {Q}.\) 
